Mathematical analysis. Lecture 1

1. Mathematical analysis (3 term)

Lectures – 26 hours
Practice -24 hours
Test (зачет)
Auto-test conditions –
Practical works and 2 control tests
Teacher – associate professor Usmanova
Angelika Rashitovna, Ph.D.
vk.com/id41101848
[email protected]

2. Structure of course

• Multivariable functions (recall)
• Multiple integrals
• Differential equations
• Line integrals

3. Multivariable functions.

4.

5.

6.

y
5
0
5
x

7.

y
0
-2/3
x

8.

y
0
x

9.

10. Level curves

11.

12.

13. Multivariable functions. Partial derivatives and partial differentials

14. Partial derivatives

Notations of partial derivatives
(in relation to х)
Analogically
partial derivatives
(in relation to y)
Notations of partial derivatives (in relation to y)

15. Examples

16.

17. Total increment

18.

19.

Definition. The linear part of formulas (4)
and (5) is called total differential and denotes as
(1.6)
or
(1.6*)
Each of addends in formula 6 is called partial differential. So, the total
differential is the sum of partial differentials. And independent increments are
equal to its differentials (as for function od one variable).

20.

21. Approximation using total differential